Nicholas Lash has an excellent account of what doing theology means today in his series of lecture Holiness, Speech and Silence: Reflections on the Question of God.
... continuing to hold the Gospel's truth makes much more serious and dangerous demands than mere lip-service paid to undigested information. Unless we make the truth our own through prayer, thought and argument - through prayer and study and an unflinching quest for understanding - it will be chipped away, reshaped, eroded by the power of an imagining fed by other springs, tuned to quite different stories. And this unceasing, strenuous, vulnerable attempt to make sone Christian sense of things, not just in what we say, but in the ways in which we 'see' the world, is what is known as doing theology. (4)For a helpful unpacking of some of the themes in this fine piece of theology, see Simon Barrow's paper What Difference does God make today?